If the objects are all at the same distance from the center of the Earth, then the gravitational forces between the Earth and each object only depend on the mass of each object. Those forces are least for the 5kg object, and greatest for the 2,540kg object.
The gravitational force that attracts each object toward the center of the Earth is typically referred to as the object's "weight".
It's important to know that there's another force of gravity ... the one that attracts the Earth toward the object. And that one is equal to the object's weight, but pulls in the opposite direction.
Your weight on the Earth is equal to the Earth's weight on you.